Big Duck wrote:> I am going to learn DSP! > > I have been studying it for a few weeks (I have many years of RF under my > belt). > > I note that the impule function in a given window has a frequency response > that is equal at every frequency in the DFT window.Correct> > I also know that white noise has a frequency response that has roughly equal > magnitude across the sample frequencies in an FFT.Here we have to get picky. White noise has an _expected_ frequency response that's equal in magnitude across the sample frequencies in an FFT. For any one measurement, though, each bin will have a considerable variation -- in general an FFT of a sample vector of white noise is _not_ at all flat.> > I am trying to make some sense of this. Here are some thoughts on this. > Please shoot down or verify: > > 1. If you took an FFT of an impulse response but randomized the phase of > each frequency in the FFT then you would get a time function that looked > like white noise ?Yes, but I doubt that it's distribution would be Gaussian, since Gaussian white noise doesn't give a constant-amplitude frequency response for a single real sample vector. Perhaps it would be Gaussian, which would make me ask if there is some other time-domain characteristic to it that's different from 'real' white noise. It would be an interesting exercise to see just what you _would_ get.> > 2. The ear does not disriminate phase (so i have been told): > If you played white noise , or if you played a properly windowed (digital) > impulse function at the right sample frequency , then it would sound > (roughly)the same to your ear.Yes and no. The ear doesn't discriminate phase to a point, but when the envelope variations get low enough (certainly 20Hz, probably higher, I don't know what the cutoff is) you start to notice.> > 3. It might be even better if you played an 1/128 impulse at a sample freq > of 10 KHz and every period you jittered the location of the impulse signal? > > > Sorry if my DSP lingo is not quite right, but tell me if this equivelance of > white noise/impulse function is true?You are confusing spectrum with distribution. Impulse noise that occurs at random times (i.e. a Poisson distribution) will be white, but without lots of filtering it _won't_ be Gaussian. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html